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Teaching Linear Algebra in a Mechanized Mathematical Environment

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Intelligent Computer Mathematics (CICM 2023)


This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the “old fashioned way”. We discuss some technological tools such as Maple, Matlab, Python, and Jupyter Notebooks, and some choices of topics that are especially suited to teaching with these tools. The discussion is informed by our experience over the past thirty or more years teaching at various levels, especially at the University of Western Ontario.

Supported in part by NSERC and by the MICINN.

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  1. 1.

    The diversity of where our students go afterwards makes it tricky to choose motivating applications. Network flow problems will appeal to a subset of people; electrical circuits might appeal to another subset. Markov chains are fun for some. Very few applications are interesting to everybody.

  2. 2.

    We resisted the temptation to call it “2” trivial.

  3. 3.

    They quite like Maple’s command, which transforms linear equations with variables into matrix-vector equations. We try to be careful to introduce this only after the students have some experience in doing the transformation by hand.

  4. 4.

    One of us teaches Cramer’s Rule only because of this beautiful proof. Cramer’s Rule itself is not particularly useful computationally nowadays, except in very special situations. But that proof is so beautiful. The students seem to like it, too.

  5. 5.

    A simple web search for “Math 1600 Western” brings the entire exam up, if you wish to see the entire context.


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This work was partially supported by NSERC under RGPIN-2020-06438 and RGPIN-2018-06670 and by the grant PID2020-113192GB-I00 (Mathematical Visualization: Foundations, Algorithms and Applications) from the Spanish MICINN. We also acknowledge the support of the Rotman Institute of Philosophy. We thank the referees for their thoughtful and constructive comments.

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Correspondence to Azar Shakoori .

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Corless, R.M., Jeffrey, D.J., Shakoori, A. (2023). Teaching Linear Algebra in a Mechanized Mathematical Environment. In: Dubois, C., Kerber, M. (eds) Intelligent Computer Mathematics. CICM 2023. Lecture Notes in Computer Science(), vol 14101. Springer, Cham.

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